Package trays usually are mounted on the body structure of an automotive vehicle between the rear seat back and the rear window. Package trays must be sufficiently strong and rigid to support small objects as well as speakers, speaker grills, glove boxes, a third stop light, and the like. However, because they are also somewhat flexible and often not fully supported by the vehicle body structure, they have a tendency to vibrate when the vehicle is in motion and in some instances when it is idling. Moreover, the underlying sheet metal of the vehicle also frequently vibrates particularly when the vehicle is not moving but the engine is running. Rattling frequently occurs when the package tray and/or the underlying vehicle sheet metal vibrates so one strikes the other. Package trays currently in use are not constructed in a manner which effectively eliminates this rattling.